Two quantities p and q are connected by a linear relation of the form p=kq+c where c and k are constant a. If q=50 when p=20 q =340 when p= 100 find the equation connecting p and q
To find the equation connecting p and q, we can use the given information to form a system of equations:
From the first condition, when p = 20 and q = 50:
20 = k(50) + c
From the second condition, when p = 100 and q = 340:
100 = k(340) + c
We now have a system of equations:
20 = 50k + c ----(1)
100 = 340k + c ----(2)
We can solve this system to find the values of k and c.
To eliminate the variable c, we subtract equation (1) from equation (2):
100 - 20 = 340k + c - (50k + c)
80 = 290k
k = 80/290
k = 8/29
Now, substitute the value of k into either equation (1) or (2) to find the value of c.
Using equation (1):
20 = 50(8/29) + c
20 = 400/29 + c
Multiply both sides by 29 to get rid of the fraction:
20 * 29 = 400 + 29c
580 = 400 + 29c
Subtract 400 from both sides:
580 - 400 = 29c
180 = 29c
c = 180/29
Therefore, the equation connecting p and q is:
p = (8/29)q + (180/29)